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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On subgroups of the multiplicative group of skew fields
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by A. Lichtman PDF
Proc. Amer. Math. Soc. 63 (1977), 15-16 Request permission

Abstract:

We give an example of a skew field D for which the multiplicative group ${D^ \ast }$ of D contains a finitely generated subgroup which satisfies a nontrivial identity and has no solvable normal subgroup of finite index. It gives a negative answer to a question of S. Bachmuth.
References
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  • M. F. Newman (ed.), Proceedings of the Second International Conference on the Theory of Groups, Lecture Notes in Mathematics, Vol. 372, Springer-Verlag, Berlin-New York, 1974. Held at the Australian National University, Canberra, August 13–24, 1973; With an introduction by B. H. Neumann. MR 0344315
  • A. I. Lichtman, On embedding of group rings in division rings, Israel J. Math. 23 (1976), no. 3-4, 288–297. MR 432692, DOI 10.1007/BF02761806
  • D. J. S. Robinson, Finiteness conditions and generalized soluble groups, Vols. 1, 2, Springer-Verlag, Berlin and New York, 1972. MR 48 #11314, 11315.
  • Gilbert Baumslag, Wreath products and extensions, Math. Z. 81 (1963), 286–299. MR 151518, DOI 10.1007/BF01111576
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 63 (1977), 15-16
  • MSC: Primary 20H20; Secondary 16A18
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0447432-0
  • MathSciNet review: 0447432